England's head of women's rugby, Rachael Burford, was among the critics online to slam the man's actions that took place in front of children - including young girls.
In a comment responding to a Tweet by freelance sports reporter, producer and presenter, Laura-Jane Jones, Burford called the man's actions "vile".
"And to the friends that were with him you are also guilty. VILE," she wrote.
Stuff reported New Zealand Rugby said in a statement that the streaker was able to get on to the pitch despite venue-specific security.
A Rugby World Cup 2021 spokesperson told the outlet precautions were taken to prevent security breaches "however in this rare instance we were unable to stop a pitch invader from accessing the field."
They said team and fan experience was a top priority.
"[...] and we will be redoubling our efforts following Saturday's incident and security staff have already been briefed to remain extra vigilant at upcoming match days.
"It is disappointing that, despite efforts to ensure Rugby World Cup 2021 provides a family-friendly and inclusive match-day experience, the actions of an individual has drawn attention away from the incredible display of women's rugby we witnessed during the quarterfinals."
The spokesperson confirmed poor behaviour at matches would not be tolerated and fans who invaded the pitch would be prosecuted, face a hefty fine or even jail time, and be trespassed from subsequent sporting fixtures.
Organisers confirmed security would be tightened to prevent actions happening again at this weekend's semifinals between the Black Ferns and France; Canada and England at Eden Park in Auckland.
